present value of a growing annuity - Maple Help

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Finance[growingannuity] - present value of a growing annuity

Calling Sequence

growingannuity(cash, rate, growth, nperiods)

Parameters

cash

-

amount of first payment

rate

-

interest rate

growth

-

rate of growth of the payments

nperiods

-

number of payments

Description

• 

The function growingannuity calculates the present value at period=0, of an annuity of nperiods payments, starting at period=1 with a payment of cash. The payments increase at a rate growth per period.

• 

Since growingannuity used to be part of the (now deprecated) finance package, for compatibility with older worksheets, this command can also be called using finance[growingannuity]. However, it is recommended that you use the superseding package name, Finance, instead: Finance[growingannuity].

Examples

I hold an investment that will pay me every year for 5 years starting next year. The first payment is 100 units, and each payment is expected to grow by 3% each year. If the interest rate is 11%, what is the present value of the investment.

withFinance:

growingannuity100,0.11,0.03,5

390.0340764

(1)

This can also be calculated as follows.

The cash flows are given by:

cf:=100,1001.03,1001.032,1001.033,1001.034

cf:=100,103.00,106.0900,109.272700,112.5508810

(2)

or equivalently as

i:='i':

cf:=seqfuturevalue100,0.03,i,i=0..4

cf:=100.0,103.00,106.0900,109.272700,112.5508810

(3)

cashflowscf,0.11

390.0340762

(4)

Here, we deal with a more complicated example illustrating differential growth. We have an investment that will pay dividends of 1.12 units starting one year from now, growing at 12 % per year for the next 5 years. From then on, it will be growing at 8%. What is the present value of these dividends if the required return is 12%? Solution: first part, the present value for the first 6 years is a growing annuity

part1:=growingannuity1.12,0.12,0.12,6

part1:=6.000000000

(5)

The fact that this is 6 times the present value of the first dividend is because the growth rate is equal to the required return. The second part, is a (deferred) growing perpetuity. Six years from now, the dividends will be

div_6:=futurevalue1.12,0.12,5

div_6:=1.973822685

(6)

So, the growing perpetuity, will start with dividends of

div_7:=futurevaluediv_6,0.08,1

div_7:=2.131728500

(7)

Its value 6 years from now is

part2_6:=growingperpetuitydiv_7,0.12,0.08

part2_6:=53.29321250

(8)

Which has a present value of

part2:=presentvaluepart2_6,0.12,6

part2:=27.00000000

(9)

Therefore the investment has a present value of

part1+part2

33.00000000

(10)

33 units.

See Also

Finance, Finance[annuity]


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